The evolution equation is solved analytically and one final numerical contour integral around the
singularities of the corresponding problem delivers the evolved flavor non–singlet structure function in
\(x\)  space. We first consider the flavor decomposition to provide realistic input distributions and derive
the corresponding evolution operators for the structure function. Here we also discuss the remainder systematics
of the yet not completely known four–loop non–singlet splitting functions \(P^{\rm NS, (3), \pm }\) .
Finally we are providing numerical results in the unpolarized and polarized case. Precision analyses of this
kind can be performed in the physics programme at the future collider experiments at the EIC [1]}
and LHeC [2]}.
